Journal ArticleDOI
Practical method for determining the minimum embedding dimension of a scalar time series
TLDR
A practical method to determine the minimum embedding dimension from a scalar time series that has the following advantages: does not contain any subjective parameters except for the time-delay for the embedding.About:
This article is published in Physica D: Nonlinear Phenomena.The article was published on 1997-12-01. It has received 1485 citations till now. The article focuses on the topics: Embedding & Scalar (mathematics).read more
Citations
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Journal ArticleDOI
Recurrence plots for the analysis of complex systems
TL;DR: The aim of this work is to provide the readers with the know how for the application of recurrence plot based methods in their own field of research, and detail the analysis of data and indicate possible difficulties and pitfalls.
Journal ArticleDOI
Transfer entropy--a model-free measure of effective connectivity for the neurosciences
TL;DR: Transfer entropy (TE) improved the detectability of effective connectivity for non-linear interactions, and for sensor level MEG signals where linear methods are hampered by signal-cross-talk due to volume conduction.
Journal ArticleDOI
A Wavelet-Chaos Methodology for Analysis of EEGs and EEG Subbands to Detect Seizure and Epilepsy
TL;DR: It is observed that while there may not be significant differences in the values of the parameters obtained from the original EEG, differences may be identified when the parameters are employed in conjunction with specific EEG subbands.
Journal ArticleDOI
Long-term time series prediction with the NARX network: An empirical evaluation
TL;DR: It is shown that the original architecture of the NARX network can be easily and efficiently applied to long-term (multi-step-ahead) prediction of univariate time series and consistently outperforms standard neural network based predictors, such as the TDNN and Elman architectures.
Proceedings ArticleDOI
Chaotic Invariants for Human Action Recognition
TL;DR: An action recognition framework that uses concepts from the theory of chaotic systems to model and analyze nonlinear dynamics of human actions and a new set of features to characterize non linear dynamics ofhuman actions is introduced.
References
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Journal ArticleDOI
Deterministic nonperiodic flow
TL;DR: In this paper, it was shown that nonperiodic solutions are ordinarily unstable with respect to small modifications, so that slightly differing initial states can evolve into considerably different states, and systems with bounded solutions are shown to possess bounded numerical solutions.
Journal ArticleDOI
Ergodic theory of chaos and strange attractors
Jean-Pierre Eckmann,David Ruelle +1 more
TL;DR: A review of the main mathematical ideas and their concrete implementation in analyzing experiments can be found in this paper, where the main subjects are the theory of dimensions (number of excited degrees of freedom), entropy (production of information), and characteristic exponents (describing sensitivity to initial conditions).
Journal ArticleDOI
Characterization of Strange Attractors
TL;DR: In this article, a measure of strange attractors is introduced which offers a practical algorithm to determine their character from the time series of a single observable, and the relation of this measure to fractal dimension and information-theoretic entropy is discussed.
Journal ArticleDOI
Independent coordinates for strange attractors from mutual information.
TL;DR: In this paper, the mutual information I is examined for a model dynamical system and for chaotic data from an experiment on the Belousov-Zhabotinskii reaction.
Journal ArticleDOI
Oscillation and Chaos in Physiological Control Systems
Michael C. Mackey,Leon Glass +1 more
TL;DR: First-order nonlinear differential-delay equations describing physiological control systems displaying a broad diversity of dynamical behavior including limit cycle oscillations, with a variety of wave forms, and apparently aperiodic or "chaotic" solutions are studied.